Tính nhanh: a/ 31.64+7.30+146.31 b/ 2^3.3^2.28+2^3.3^5.8
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c) Ta có: x+11 chia hết cho x+1
x+1+10 chia hết cho x+1
Vì x+1 chia hết cho x+1 nên 10 chia hết cho x+1.
Vậy x+1\(\inƯ\left(10\right)=\left\{1;2;5;10\right\}\)
\(\Rightarrow x\in\left\{0;1;4;9\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^3.3^2.28+2^3.3^5.8\\ =2^3.3^2.2^2.7+2^3.3^5.2^3\\ =2^5.3^2.7+2^6.3^5\\ =2^5.3^2\left(7+2.3^3\right)\\ =32.9\left(7+54\right)\\ =32.9.61=17568\)
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a) 15+25+35+...+115
(115-15):5+1=21 số hạng
(115+15).21:2=1365
a: Số số hạng là (115-15):10+1=11(số)
Tổng là (115+15)*11/2=65*11=715
b: =31(64+146)+210
=210(31+1)
=210*32=6720
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\(B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+....+100\left(101-1\right)\)
\(=1.2+2.3+3.4+...+100.101-\left(1+2+3+...+100\right)\)
Ta có: \(M=1.2+2.3+...+100.101\)
\(3M=1.2.\left(3-0\right)+2.3.\left(4-1\right)+...+100.101\left(102-99\right)\)
\(=-0.1.2+1.2.3-1.2.3+2.3.4-...-99.100.101+100.101.102\)
\(=100.101.102\)
\(\Rightarrow M=\frac{100.101.102}{3}=343400\)
\(N=1+2+...+100=\frac{\left(100+1\right).100}{2}=5050\)
\(B=M-N=338350\)
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\(a.271.11-17.11\)
\(=\left(271-17\right).11\)
\(=254.11\)
\(=2794\)
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a, \(4^7.3^4.9^6:6^{13}\)
\(=\left(2^{14}.3^4.3^{12}\right):\left(2^{13}.3^{13}\right)\)
\(=2^{14}:2^{13}.3^{16}:3^{13}\)
\(=2.3^3=54\)
b, \(2^3.3^2-5^{16}:25^7\)
\(=72-5^{16}:5^{14}\)
\(=72-5^2=47\)
a/
31.64+7.30+146.31=31.(64+146)+7.30
=31.210+7.30=6510+210=6720
b/23.32.28+23.35.8=23.(32.28+35.8)
=23.(9.28+243.8)=8.(252+1944)
=8.2196=17568